A new model of strategy-making as play is presented in response to increasing calls for a deeper theory of strategy-making. First an elaboration of the construct of strategic imagination is offered, describing three distinct, but interrelated forms of imagination: descriptive, creative, and challenging. Strategic Imagination is defined as an emergent property of a complex interplay between the three kinds of imagination. Then, extending the work of the planning and design schools, the model describes the complex social dynamic of strategy-making itself. Applying the notion of play from anthropology and cognitive development, the strategy-making process is described as a three-phase play process. The three phases, constructing to stimulate new ideas, story telling to share meaning, and deep engagement to assimilate new directions, are described. Finally some directions for strategy-making practice improvement are offered.